A multi-start evolutionary local search for the one-commodity pickup and delivery traveling salesman problem

This article addresses the one-commodity pickup and delivery traveling salesman problem (1-PDTSP), which is a generalization of the well-known traveling salesman problem. The 1-PDTSP aims to find a Hamiltonian tour in which a set of supply points (pickup locations), demand points (delivery locations) are visited and, the total traveled distance is minimized. We propose a hybrid metaheuristic based on multi-start evolutionary local search and variable neighborhood descent to solve the 1-PDTSP. To test the performance of our algorithm, we solve instances with up to 500 nodes available in the literature and we demonstrate that our approach is able to provide competitive results when comparing to other existing strategies. Since a direct application of the 1-PDTSP arises as the bicycle repositioning problem, we also use our metaheuristic algorithm to solve a set of real-case instances based on EnCicla, the bicycle sharing system in the Aburrá Valley (Antioquia, Colombia).